You will need to cut the eye pin since it is too long for the base of the eye pin to be flush with the surface of the hair stick.

Place an extra head or eye pin in the hole at the top of the hair stick until it won't go any further, and mark the location on this pin at the surface of the hair stick. Mark this same length on the eye pin and cut it.

Add a dab of adhesive to the eye pin, add the bead cap and glue it into the hole.